Numerical answer to Partial derivative of Hopfield-style Energy in symbolic expression

2 次查看（过去 30 天）
Pseudoscientist
Pseudoscientist 2022-7-28
评论： Torsten 2022-8-2
Hello,
I'm implementing a gradient descent optimizer that uses Hopfield-style energy as function,
the hopfield-style energy is a function of p:
The hopfield energy equation can also be expressed as:
The gradient vector is defined as:
I'm attempting to calculate the gradient vector using the Symbolic Toolbox as follows:
r_mat = sym('r',[4,4]);
r_mat = r_mat(:);
p_mat = sym('p',[4*4,1]);
c_mat = sym('c',[4*4,1]);
Energy = -0.5*p_mat'*r_mat*p_mat' - c_mat'*p_mat;
%the first partial derivative:
q1 = -1*diff(testi1,p_mat(1,1));
which yields as the first term:
conj(c1) + r1_1*conj(p1) + (r1_2*conj(p5))/2 + (r1_3*conj(p9))/2 + (r2_1*conj(p2))/2 + (r1_4*conj(p13))/2 + (r2_2*conj(p6))/2 + (r2_3*conj(p10))/2 + (r3_1*conj(p3))/2 + (r2_4*conj(p14))/2 + (r3_2*conj(p7))/2 + (r3_3*conj(p11))/2 + (r4_1*conj(p4))/2 + (r3_4*conj(p15))/2 + (r4_2*conj(p8))/2 + (r4_3*conj(p12))/2 + (r4_4*conj(p16))/2
How can I replace the symbols with numbers to yield the q vector? I need the q-vector for the gradient descent
the algorithm I'm implementing: https://doi.org/10.1117/1.JEI.23.1.013007 (relevant part starts at Equation 5)

请先登录，再回答此问题。

采纳的回答

Torsten
Torsten 2022-7-28
编辑：Torsten 2022-7-28
p is (4x1), not (16x1).
And keep r_mat as matrix, then
E = -0.5*p.'*r_mat*p - c.'*p
( r_mat can be assumed symmetric ).
By the way:
dE/dp = -r_mat*p - c
assuming r_mat is symmetric.
To replace symbols by numerical values, use "subs".
  5 个评论
显示 3更早的评论
Pseudoscientist
Pseudoscientist 2022-8-2
It turned out symbolic expressions was extremely slow, I used symbolic to calculate the partial derivative and then used that to think how to write the equation in vector form and was evetually succesful and the optimizer is now very fast !
Torsten
Torsten 2022-8-2
I used symbolic to calculate the partial derivative and then used that to think how to write the equation in vector form
That's the best you can do, I guess.

请先登录，再进行评论。

更多回答（0 个）

类别

在 Help Center 和 File Exchange 中查找有关 Calculus 的更多信息

标签

产品

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by